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Exploring Sequential Modules and Counters: Application and Design

This lecture delves into sequential modules such as shift registers, counters, and their applications like program counters and clocks. Learn how to design counters for different scenarios, including cascade counters and modulo-n counters.

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Exploring Sequential Modules and Counters: Application and Design

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  1. CS 140 Lecture 19Sequential Modules Professor CK Cheng CSE Dept. UC San Diego

  2. Standard Sequential Modules • Register • Shift Register • Counter

  3. Counter • Applications?

  4. Counter: Applications • Program Counter • Address Keeper: FIFO, LIFO • Clock Divider • Sequential Machine

  5. Counter • Modulo-n Counter • Modulo Counter (m<n) • Counter (a-to-b) • Counter of an Arbitrary Sequence • Cascade Counter

  6. Modulo-n Counter D CNT TC LD Clk CLR Q Q (t+1) = (0, 0, .. , 0) if CLR = 1 = D if LD = 1 and CLR = 0 = (Q(t)+1)mod n if LD = 0, CNT = 1 and CLR = 0 = Q (t) if LD = 0, CNT = 0 and CLR = 0 TC = 1 if Q (t) = n-1 and CNT = 1 = 0 otherwise

  7. Q3 Q2 Q1 Q0 3 2 1 0 CLR CLK CNT X D3 D2 D1 D0 LD Q2 0 0 0 0 Q0 Modulo-m Counter (m< n) Given a mod 16 counter, construct a mod-m counter (0 < m < 16) with AND, OR, NOT gates m = 6 Set LD = 1 when X = 1 and (Q3Q2Q1Q0) = (0101), ie m-1

  8. Counter (a-to-b) Given a mod 16 counter, construct an a-to-b counter (0 < a < b < 15) A 5-to-11 Counter Q3 Q2 Q1 Q0 CLR Clk CNT X D3 D2 D1 D0 LD Q3 (b) Q1 0 1 0 1 (a) Q0 Set LD = 1 when X = 1 and (Q3Q2Q1Q0) = b (in this case, 1011)

  9. Q2 Q1 Q0 CLR Clk CNT X D2 D1 D0 LD Q2’ Q0 Q0 Q1 Q0 Q2 Q0’ Counter of an Arbitrary Sequence Given a mod 8 counter, construct a counter with sequence 0 1 5 6 2 3 7 When Q = 1, load D = 5 When Q = 6, load D = 2 When Q = 3, load D = 7

  10. Counter of an Arbitrary Sequence Given a mod 8 counter, construct a counter with sequence 0 1 5 6 2 3 7 K Mapping LD and D, we get LD = Q2’ Q0 + Q2Q0’ D2 = Q0 D1 = Q1 D0 = Q0

  11. Counter of an Arbitrary Sequence Example: Count in sequence 0 2 3 4 5 7 6 LD = 1 D = 2 When Q(t) = 0 LD = 1 D = 7 When Q(t) = 5 LD = 1 D = 6 When Q(t) = 7 LD = 1 D = 0 When Q(t) = 6 Through K-map, we derive LD = Q2’ Q1’ + Q2Q0 + Q2 Q1 D2 = Q0 D1 = Q1’ + Q0 D0 = Q1’Q0

  12. Cascade Counter A Cascade Modulo 256 Counter Q7,Q6,Q5,Q4 Q3,Q2,Q1,Q0 TC0 CNT LD CNT LD X TC TC Clk Clk D7,D6,D5,D4 D3,D2,D1,D0

  13. Cascade Counter TC = 1 when (Q3,Q2,Q1,Q0 )=(1,1,1,1) and X=1 (Q7 (t+1)Q6 (t+1) Q5 (t+1) Q4 (t+1)) = (Q7 (t)Q6 (t) Q5 (t) Q4 (t)) + 1 mod 16 when TC0 = 1 The circuit functions as a modulo 256 counter.

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